The data shown to the right was procured using a light probe and a flickering candle in a completely darkened room. The x-axis has no relevance except to indicate that the data was collected within 60 seconds. The y-axis represents the number of lumens/m2, or lux, that illuminated the probe's surface area.

The "plateaus" represent unique distances, or stations, at which the probe was positioned during the procurement of data. The distances are given in the data table shown below.

You first task is to determine an "average" value for the number of lux at each station. You will probably need to print the graph and then interpolate the heights of each plateau since they do not "exactly line up" with the grid lines provided.

Then you will graphically analyze the relationship between the magnitudes of the illumination and the distance from the light source. You may use a graphing program, such as EXCEL, or you can graph your data by hand on graph paper.

When a light source emits light, the light "expands" as an ever-growing light sphere. The illuminance represents the number of luminous flux (light rays) that fall on each square meter of the sphere's surface area.

Since the number of lumens emitted by the source is independent of the light sphere's growing size, we can write the following relationship:

This final formula tells us that the illuminance varies inversely as the square of the distance from the source. This is the same relationship as the force of gravity between two point masses and the electrostatic force between two point charges. The intensity of sound (in watts/m2) also obeys this relationship.

Summary Questions

Calculate the surface area of a sphere having a radius of 0.20 meters.

Using the equation from your graph of
Illuminance vs 1/Distance2, calculate the illumination, or lux, impinging on a square meter of this sphere's surface.

Using the information from the previous two questions, calculate the number of lumens released by the candle's flame.

Discuss the disadvantages of using a "candle" as a light source. Can you see when it was "flickering" in the data?